1. Field of the Invention
The invention relates generally to the field of optical sensing of physical parameters. More specifically, the invention relates to methods for demodulating optical path differences of a dispersive white light interferometric sensor to determine the value of parameter measured by the sensor.
2. Background Art
Optical sensors generate a signal that causes a property of light passed through the sensor to correspond in a determinable manner to a parameter measured by the sensor. One such sensor is known as an extrinsic fiber Fabry Perot interferometric (“EFPI”) sensor. The basic structure of EFPI sensors is described in Bing Qi, et al., Novel data processing techniques for dispersive white light interferometer, Optical Engineering 42(11), pp. 3165-3171 (November 2003), Society of Photo-Optical instrumentation Engineers. In an EFPI sensor, a lead in fiber and a reflected fiber are bonded inside a glass tube such that ends of the lead in and reflected fibers are separated by a small air gap. Changes in the ambient environment on the glass tube change the air gap. A broadband light source is applied to the lead in fiber, some of which is reflected by the fiber end and other portions of which are reflected by the end of the reflected fiber. Combination of both reflected light portions in the lead in fiber creates an interference pattern that is related to the size of the air gap, and thus to the physical parameter being measured by the EFPI sensor.
Various techniques are known in the art for converting the interference pattern into an optical path difference (“OPD”) for dispersive white light interferometry, and correspondingly, the magnitude of the measured parameter. One such technique is described in the Qi et al. paper cited above. Other techniques are described in, J. Schwindler et al., Dispersive interferometric profiler, Optics Letters, vol. 19, no. 13, (1994) Optical Society of America, and in U. Schnell et al., Dispersive white light interferometry for absolute distance measurement with dielectric multilayer systems on the target, Optics Letters, vol. 21, no. 7 (1996), Optical Society of America. Still other techniques are described in J. Tapia-Mercado et al., Precision and Sensitivity Optimization for White-Light Interferometric Fiber-Optic sensors, J. Lightwave Tech., vol. 19, no. 1 (2001) Institute of Electrical and Electronics Engineers and M. Hart et al., Fast surface profiling by spectral analysis of white-light interferograms with Fourier transform spectroscopy, Applied Optics, vol. 37, no. 10 (1998) Optical Society of America.
The foregoing techniques are intended to determine the optical path differences on a particular sensor by direct analysis of the interference pattern returned by the sensor. In a practical application of EFPI sensors, such as monitoring parameters in a wellbore drilled through Earth formations, the length of the lead in fiber, which can be several kilometers, can make it difficult to resolve the spectrum of the interference pattern due to a far reduced visibility of the interference spectrum and other noise components. What is needed is a technique that can resolve the interference pattern to determine the length of the air gap in an EFPI sensor even under conditions as would ordinarily be expected in wellbores drilled into the Earth. There continues to be a need for high accuracy, high precision demodulation methods for use in other dispersive, white light interferometric sensors, including, for example, Michelson and Mach-Zender interferometers having optical path difference related to the parameter being measured.